Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Applied Physics

Two-site Hubbard molecule with a spinless electron-positron pair

Fabrizio Cossu, C. Schuster, Udo Schwingenschlögl

Published Dec 15, 2012• 0 citations
Publisher

Abstract

We determine the eigenvalues of the two-site Hubbard molecule with one electron and one positron to describe the characteristics of electron-positron interactions in solids. While the effect of hopping is, in general, opposite to the effect of on-site interaction, we find a complex scenario for the electron-positron pair with a non-vanishing potential drop. We give analytical solutions and discuss the combined effects of the model parameters.

DOI
10.1063/1.4769741

Related papers

The atomic method for the Hubbard dimer

Renan Lira Nunes, Marcos Sergio Figueira da Silva

The single-band Hubbard Hamiltonian [1] is the simplest model of interacting electrons in a lattice.It was developed by John Hubbard, who introduced the model to take into account the local electronic correlations in narrow energy bands.The model has a kinetic term that allows hopping of electrons between atomic sites and a term that considers the on-site interaction between electrons.This model is largely used in solid state physics to study magnetic properties of solids, insulator-metal transition (Mott transition) and high temperature superconductors.However, this is a problem that has exact analytical solution in a very few limiting cases and must be treated approximately or numerically.In this work, we propose a new methodology to analytically solve the Hubbard Hamiltonian, mapping it into a two-site model (the Hubbard dimer).To obtain the Green's function for the lattice, we employed the cumulant expansion technique, using as a 'seed' the exact two-site Green's function (the atomic method) [2].From the Green's function, we obtained the density of states [DOS] and the occupation numbers as functions of the external parameters of the model, and compared the results with the Hubbard I approximation [1].

Brazilian Workshop on Semiconductor Physics•Aug 19, 2017•1 citation

Investigation of on-site interorbital single-electron hoppings in general multiorbital systems

Qingguo Feng, P. M. Oppeneer

A generalized multiorbital Hubbard model, which includes on-site interorbital electron hoppings, is introduced and studied on an arbitrary basis. In a general system the on-site interorbital single-electron hopping may exist realistically between two orbitals, e.g., the excitation of electrons or flow of electrons between two hybridized states, and is hence one of the most basic interactions like the intersite hopping and the on-site Coulomb interactions. It is shown in this work how the higher order interactions can be well incorporated (or generated) in the equations of motion from the basic interactions in the Hamiltonian, which has made it possible and also given a self-consistent way to investigate these higher order correlation effects. The two-orbital Hubbard model is studied numerically in the paramagnetic case to demonstrate the influence of the single-electron hopping effect, leading to a change of the shape of the bands and a shrinking of the difference between the two bands. Inclusion of the on-site interorbital hopping suppresses the so-called orbital-selective Mott transition.

arXiv:1110.4045•Physical Review B•Jul 6, 2012•4 citations

Small-cluster calculations for the simple and extended Hubbard models

J. Callaway, D. P. Chen, D. G. Kanhere +1 more

The single-band Hubbard model (both with and without first-neighbor interactions) is studied by exact diagonalization on several one- and two-dimensional clusters, ranging from four to nine sites, including rings and arrangements of squares. Occupancies include the half-filled band (one electron per site) and configurations with one and two holes in the half-filled band. Ground-state properties are determined for a wide range of parameters. We discuss the phase diagram in the (U,V) plane and consider spin, charge, and pairing correlations. The binding of a pair of holes is investigated. Circumstances in which binding and pairing are enhanced by first-neighbor interactions are described.

Physical review. B, Condensed matter•Jul 1, 1990•41 citations

THE EFFECT OF A BOND-SITE INTERACTION ON THE GROUND-STATE INSTABILITIES OF THE ONE-DIMENSIONAL HUBBARD MODEL

Florin D. Buzatu

The ground-state instabilities for a one-dimensional lattice system of electrons with onsite (Hubbard) and bond-site (hopping) interactions are analyzed in a perturbative approach. The zero temperature phase diagram at different band fillings is drawn; an attractive (repulsive) bond-site interaction favors the appearance of a superconductor state at low concentrations of electrons (holes). A comparison with the exact results for the Hubbard model and previous works for particular cases is also discussed.

International Journal of Modern Physics B•May 30, 1995•3 citations

Hubbard Model

James K. Freericks

The Hubbard model is one of the most important models of many-body physics. It is a simplified model for how electrons move and interact in a crystal. It consists of a hopping term, where electrons can move between neighboring sites (sometimes more distant neighbors are allowed). When two electrons (of opposite spin) occupy the same lattice site, they feel a Coulomb repulsion. This model can be exactly solved only in one dimension, in the limit of infinite dimensions, or for small systems via exact diagonalization. It has been studied by thousands of physicists over the years. While much is known about the model, even more remains unknown, so it is still a great frontier to examine further. In this chapter, we focus on the known solutions and provide concrete examples and rigorous theorems about the behavior of the model. This includes the symmetries of spin, particle number, and pseudospin, the Nagaoka theorem for ferromagnetism, spin-reflection positivity, and spin and pseudospin towers.

Springer eBooks•Jan 1, 2026•0 citations

EFFECT OF CORRELATED-HOPPING INTERACTION ON A ONE-DIMENSIONAL EXTENDED HUBBARD MODEL WITH SPIN-EXCHANGE INTERACTION

Hanqin Ding, Jun Zhang

By using the field-theoretical techniques combining bosonization with renormalization group, we study a one-dimensional (1D) model of interacting electrons with on-site repulsion (U > 0), nearest-neighbor (nn) exchange (J) and correlated-hopping (t2, t3) interactions at weak coupling. In the case of a half-filled band, the two-body interaction t2 does not influence phase diagram of the model, while the presence of three-body interaction t3 makes the physics of the system highly non-trivial. By a Hartree–Fock decoupling, the effects of t3 bring about hopping of pairs, V-like (nn Coulomb interaction) and isotropic exchange terms in the reduced model Hamiltonian. Interestingly, a negative t3 provides a possibility for the occurrence of the triplet superconductivity in 1D system with purely repulsive interactions (U, J > 0). The ground state phase diagram including the insulating and superconducting phases is discussed analytically.

Modern Physics Letters B•Feb 20, 2012•5 citations
We determine the eigenvalues of the two-site Hubbard molecule with one electron and one positron to describe the characteristics of electron-positron interactions in solids. While the effect of hopping is, in general, opposite to the effect of on-site interaction, we find a complex scenario for the electron-positron pair with a non-vanishing potential drop. We give analytical solutions and discuss the combined effects of the model parameters.
The single-band Hubbard Hamiltonian [1] is the simplest model of interacting electrons in a lattice.It was developed by John Hubbard, who introduced the model to take into account the local electronic correlations in narrow energy bands.The model has a kinetic term that allows hopping of electrons between atomic sites and a term that considers the on-site interaction between electrons.This model is largely used in solid state physics to study magnetic properties of solids, insulator-metal transition (Mott transition) and high temperature superconductors.However, this is a problem that has exact analytical solution in a very few limiting cases and must be treated approximately or numerically.In this work, we propose a new methodology to analytically solve the Hubbard Hamiltonian, mapping it into a two-site model (the Hubbard dimer).To obtain the Green's function for the lattice, we employed the cumulant expansion technique, using as a 'seed' the exact two-site Green's function (the atomic method) [2].From the Green's function, we obtained the density of states [DOS] and the occupation numbers as functions of the external parameters of the model, and compared the results with the Hubbard I approximation [1].
A generalized multiorbital Hubbard model, which includes on-site interorbital electron hoppings, is introduced and studied on an arbitrary basis. In a general system the on-site interorbital single-electron hopping may exist realistically between two orbitals, e.g., the excitation of electrons or flow of electrons between two hybridized states, and is hence one of the most basic interactions like the intersite hopping and the on-site Coulomb interactions. It is shown in this work how the higher order interactions can be well incorporated (or generated) in the equations of motion from the basic interactions in the Hamiltonian, which has made it possible and also given a self-consistent way to investigate these higher order correlation effects. The two-orbital Hubbard model is studied numerically in the paramagnetic case to demonstrate the influence of the single-electron hopping effect, leading to a change of the shape of the bands and a shrinking of the difference between the two bands. Inclusion of the on-site interorbital hopping suppresses the so-called orbital-selective Mott transition.
The single-band Hubbard model (both with and without first-neighbor interactions) is studied by exact diagonalization on several one- and two-dimensional clusters, ranging from four to nine sites, including rings and arrangements of squares. Occupancies include the half-filled band (one electron per site) and configurations with one and two holes in the half-filled band. Ground-state properties are determined for a wide range of parameters. We discuss the phase diagram in the (U,V) plane and consider spin, charge, and pairing correlations. The binding of a pair of holes is investigated. Circumstances in which binding and pairing are enhanced by first-neighbor interactions are described.
The ground-state instabilities for a one-dimensional lattice system of electrons with onsite (Hubbard) and bond-site (hopping) interactions are analyzed in a perturbative approach. The zero temperature phase diagram at different band fillings is drawn; an attractive (repulsive) bond-site interaction favors the appearance of a superconductor state at low concentrations of electrons (holes). A comparison with the exact results for the Hubbard model and previous works for particular cases is also discussed.
The Hubbard model is one of the most important models of many-body physics. It is a simplified model for how electrons move and interact in a crystal. It consists of a hopping term, where electrons can move between neighboring sites (sometimes more distant neighbors are allowed). When two electrons (of opposite spin) occupy the same lattice site, they feel a Coulomb repulsion. This model can be exactly solved only in one dimension, in the limit of infinite dimensions, or for small systems via exact diagonalization. It has been studied by thousands of physicists over the years. While much is known about the model, even more remains unknown, so it is still a great frontier to examine further. In this chapter, we focus on the known solutions and provide concrete examples and rigorous theorems about the behavior of the model. This includes the symmetries of spin, particle number, and pseudospin, the Nagaoka theorem for ferromagnetism, spin-reflection positivity, and spin and pseudospin towers.
By using the field-theoretical techniques combining bosonization with renormalization group, we study a one-dimensional (1D) model of interacting electrons with on-site repulsion (U > 0), nearest-neighbor (nn) exchange (J) and correlated-hopping (t2, t3) interactions at weak coupling. In the case of a half-filled band, the two-body interaction t2 does not influence phase diagram of the model, while the presence of three-body interaction t3 makes the physics of the system highly non-trivial. By a Hartree–Fock decoupling, the effects of t3 bring about hopping of pairs, V-like (nn Coulomb interaction) and isotropic exchange terms in the reduced model Hamiltonian. Interestingly, a negative t3 provides a possibility for the occurrence of the triplet superconductivity in 1D system with purely repulsive interactions (U, J > 0). The ground state phase diagram including the insulating and superconducting phases is discussed analytically.